The inequality |x - 1| < 4 has solution set

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Multiple Choice

The inequality |x - 1| < 4 has solution set

Explanation:
Absolute value inequalities express a distance constraint. Here, |x − 1| < 4 means x is within distance 4 of the point 1. Write -4 < x − 1 < 4 and then add 1 to all parts to get -3 < x < 5. This describes all real numbers strictly between -3 and 5, which is the open interval (-3, 5). The endpoints aren’t included because the inequality is strict. If the inequality were ≤ 4, the endpoints would be included, giving [-3, 5].

Absolute value inequalities express a distance constraint. Here, |x − 1| < 4 means x is within distance 4 of the point 1. Write -4 < x − 1 < 4 and then add 1 to all parts to get -3 < x < 5. This describes all real numbers strictly between -3 and 5, which is the open interval (-3, 5). The endpoints aren’t included because the inequality is strict. If the inequality were ≤ 4, the endpoints would be included, giving [-3, 5].

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